Origins would probably be saved for the possible solo movies, but I don't think it has to go as far as superheroes being the norm. As it was mentioned upthread, the New 52 shows the superheroes slowly emerging and being feared by the public. If this movie ties in with "Man of Steel" then he was the first emergence of a superhero, and the public was fearful of him, and after that, suddenly they start getting reports of other emerging superheroes. The New 52 started at a good point where there are reports of superheroes but I think the JL movie should show a little bit more, show the individual heroes in their cities doing what they do even if briefly, and show the reaction in these cities to their appearances. Maybe the sudden emergence of these heroes and the more public exposure of them is because there is the looming threat of Darkseid, and there are incidents occurring around the world because of his doing.

Well, Man of Steel is already teasing how the world is fearful of superheroes with the poster of Supes in cuffs as well as the leaked comic con footage of Superman stepping out of rubble with the military aiming their guns at him. So it seems they will be emulating the New 52 approach of having a world just now getting used to the idea of superpowered beings.

So I don't think nor do I hope that superheroes will be the "norm" in the world of the JL movie. However, they could be in the public eye at least like you said. Getting a glimpse of each hero doing acts of heroism in the city but the public backlashing due to the destruction that follows. A plot point could be the heroes trying to manage the level of destruction that their battles bring about.

But unlike the New 52, it could be cool if at the end of JL, the public still isn't 100% supportive of superheroes leading to the formation of Cadmus and possibly the Suicide Squad? I don't know, I'm still in kicking around ideas mode.